Major League Baseball teams (usually) play a 162-game season, during which fans are often excited by long winning streaks and frustrated by long losing streaks. But how unusual are these streaks, really? How long a streak would you expect if the team’s performance were independent from game to game?
Write a program that simulates a 162-game season, i.e., a string of 162 wins and losses, with P(win) = p for each game (the value of p to be specified later). Use your program with at least 10,000 runs to answer the following questions.
a. Suppose you’re rooting for a “.500” team—that is, p = .5. What is the probability of observing a streak of at least five wins in a 162-game season? Estimate this probability with your program, and include a standard error.
b. Suppose instead your team is quite good: a .600 team overall, so p = .6. Intuitively, should the probability of a winning streak of at least five games be higher or lower? Explain.
c. Use your program with p = .6 to estimate the probability alluded to in (b). Is your answer higher or lower than (a)? Is that what you anticipated